/*Run Online (Liu method)*/
        private void btnRunOnl_Click(List <double> training_data, List <double> streaming_data, int period, int NLength, int maxEntry, int minEntry, int R, int D)
        {
            //create a new buffer. In this demo, the buffer is training_data (edit later):
            List <double> this_buffer = new List <double>();

            this_buffer.AddRange(training_data);

            // Store furnitures in RTree
            int              this_id_item     = int.MinValue;
            List <int>       this_id_itemList = new List <int>();
            RTree <int>      this_RTree       = new RTree <int>(maxEntry, minEntry);
            List <Rectangle> this_recList     = new List <Rectangle>();

            // Call 'Run Offline' for the first time, store results into variables ("this" object):
            List <double> discord_firsttime = RunOfflineMinDist(training_data, NLength, maxEntry, minEntry, R, D, ref this_id_item, ref this_id_itemList, ref this_recList, ref this_RTree, true);

            // Store current discord in buffer
            double this_best_so_far_dist = discord_firsttime[0];
            double this_best_so_far_loc  = discord_firsttime[1];

            //store the last subsequence of the buffer:
            List <double> last_sub = this_buffer.GetRange(this_buffer.Count - NLength, NLength);


            // STREAMING: keep streaming until we have no more data points
            for (int index_stream = 0; index_stream < streaming_data.Count; index_stream++)
            {
                var watch = System.Diagnostics.Stopwatch.StartNew();///calc execution time

                double new_data_point = streaming_data[index_stream];

                //update last_sub at time t to get new_sub at time (t+1):
                last_sub.Add(new_data_point);
                last_sub.RemoveAt(0);
                List <double> new_sub = last_sub; // the same object

                // Insert the new entry into the tree:
                this_id_item++;

                // Add the new rec to the tree:
                Rectangle new_rec = new Rectangle(Utils.MathFuncs.PAA_Lower(new_sub, D, R).ToArray(), Utils.MathFuncs.PAA_Upper(new_sub, D, R).ToArray(), this_buffer.Count - NLength + 1 + index_stream);
                this_RTree.Add(new_rec, this_id_item);
                this_recList.Add(new_rec);
                this_id_itemList.Add(this_id_item);

                //remove the oldest entry:
                this_RTree.Delete(this_recList[index_stream], this_id_itemList[index_stream]);

                //get the first sub before update the buffer (help to find the small match in Liu's method)
                List <double> first_sub = this_buffer.GetRange(0, NLength);

                // update buffer:
                this_buffer.Add(new_data_point);
                this_buffer.RemoveAt(0);

                /* 'til now, we have already updated the tree.
                 * from now on, almost just copy the offline code:
                 */

                //Method 1: just re-order the 2 loops:
                //RunOnline_Method1(this_buffer, index_stream);

                //Method 2: Liu's algorithm:
                //Note: Method_2 includes method_1 (case a)
                //RunOnline_LiuMethod_origin(this_buffer, index_stream, first_sub);

                //Method 3: motified_Liu's
                List <double> discord_Liu = RunOnline_LiuMethod_edited(this_buffer, index_stream, first_sub, this_RTree, this_best_so_far_dist, (int)this_best_so_far_loc, NLength, D);
                this_best_so_far_dist = discord_Liu[0];
                this_best_so_far_loc  = discord_Liu[1];

                watch.Stop(); //stop timer
                long elapsedMs = watch.ElapsedMilliseconds;
                //this.txtExeTime.Text = elapsedMs.ToString();

                Console.WriteLine("ExeTime_Online=" + elapsedMs.ToString());

                // Useless variable to pass parameter
                int              dumb          = 0;
                List <int>       dumb_list     = new List <int>();
                List <Rectangle> dumb_rectlist = new List <Rectangle>();
                RTree <int>      dumb_rtree    = new RTree <int>(maxEntry, minEntry);



                //call offline version to assure the results and compare the time executions:
                var           watch2          = System.Diagnostics.Stopwatch.StartNew();///calc execution time offline
                List <double> discord_offline = RunOfflineMinDist(training_data, NLength, maxEntry, minEntry, R, D, ref dumb, ref dumb_list, ref dumb_rectlist, ref dumb_rtree, false);
                double        this_best_so_far_dist_offline = discord_offline[0];

                watch2.Stop(); //stop timer
                long this_exeTimeOffline = watch2.ElapsedMilliseconds;

                //check:
                if (Math.Abs(this_best_so_far_dist - this_best_so_far_dist_offline) < 10e-7)
                {
                    Console.WriteLine("checked, ok.");
                    if (elapsedMs > this_exeTimeOffline)
                    {
                        Console.WriteLine("Online takes more time than Offline !!!");
                    }
                }
                else
                {
                    Console.WriteLine("this.best_so_far_dist = " + this_best_so_far_dist);
                    Console.WriteLine("this.best_so_far_dist_Offline = " + this_best_so_far_dist_offline);
                    Console.WriteLine("The results are different. Stop Streaming !!!");
                    return;
                }

                Console.WriteLine("------------------------");
            } // end For loop (streaming)

            Console.WriteLine("--- Streaming's done (run out of data) ---");
        } //end btnRunOnl_Click function
        } //end btnRunOnl_Click function

        /*Run Online - new method (inner loop only)*/
        private void Btn_NewOnline_Click(List <double> training_data, List <double> streaming_data, int period, int NLength, int maxEntry, int minEntry, int R, int D)
        {
            //create a new buffer. In this demo, the buffer is training_data (edit later):
            List <double> this_buffer = new List <double>();

            this_buffer.AddRange(training_data);

            // Store furnitures in RTree
            int              this_id_item     = int.MinValue;
            List <int>       this_id_itemList = new List <int>();
            RTree <int>      this_RTree       = new RTree <int>(maxEntry, minEntry);
            List <Rectangle> this_recList     = new List <Rectangle>();

            // Call 'Run Offline' for the first time, store results into variables ("this" object):
            List <double> discord_firsttime = RunOfflineMinDist(training_data, NLength, maxEntry, minEntry, R, D, ref this_id_item, ref this_id_itemList, ref this_recList, ref this_RTree, true);
            double        this_best_so_far_dist_TheMostDiscord = discord_firsttime[0];

            //store the last subsequence of the buffer:
            List <double> last_sub = this_buffer.GetRange(this_buffer.Count - NLength, NLength);


            // STREAMING: keep streaming until we have no more data points
            for (int index_stream = 0; index_stream < streaming_data.Count; index_stream++)
            {
                var watch = System.Diagnostics.Stopwatch.StartNew();///calc execution time

                double new_data_point = streaming_data[index_stream];

                //update last_sub at time t to get new_sub at time (t+1):
                last_sub.Add(new_data_point);
                last_sub.RemoveAt(0);
                List <double> new_sub = last_sub; // the same object

                // Insert the new entry into the tree:
                this_id_item++;

                // Add the new rec to the tree:
                Rectangle new_rec = new Rectangle(Utils.MathFuncs.PAA_Lower(new_sub, D, R).ToArray(), Utils.MathFuncs.PAA_Upper(new_sub, D, R).ToArray(), this_buffer.Count - NLength + 1 + index_stream);
                this_RTree.Add(new_rec, this_id_item);
                this_recList.Add(new_rec);
                this_id_itemList.Add(this_id_item);

                //remove the oldest entry:
                this_RTree.Delete(this_recList[index_stream], this_id_itemList[index_stream]);

                // update buffer:
                this_buffer.Add(new_data_point);
                this_buffer.RemoveAt(0);

                /* 'til now, we have already updated the tree.
                 * from now on, almost just copy the offline code:
                 */

                //Run new_online_algorithm:
                NewOnlineAlgorithm(this_buffer, 2 * period, index_stream, period, new_sub, this_RTree, NLength, D, R, maxEntry, minEntry, ref this_best_so_far_dist_TheMostDiscord);

                watch.Stop(); //stop timer
                long elapsedMs = watch.ElapsedMilliseconds;
                //this.txtExeTime.Text = elapsedMs.ToString();

                Console.WriteLine("ExeTime_Online=" + elapsedMs.ToString());

                Console.WriteLine("------------------------");
            } // end For loop (streaming)

            Console.WriteLine("--- Streaming's done (run out of data) ---");
        }
        ////////////// Main Functions //////////////

        /*Run new offline (minDist) */
        public static List <double> RunOfflineMinDist(List <double> inputData, int NLength, int maxEntry, int minEntry, int R, int D, ref int this_id_item, ref List <int> this_id_itemList, ref List <Rectangle> this_rectList, ref RTree <int> this_RTree, bool is_first_time)
        {
            int         id_item = int.MinValue;
            RTree <int> rtree   = new RTree <int>(maxEntry, minEntry);

            List <int> candidateList   = new List <int>();
            List <int> beginIndexInner = new List <int>();
            List <int> indexOfLeafMBRS = new List <int>();

            double best_so_far_dist = 0;
            int    best_so_far_loc  = -1;

            double nearest_neighbor_dist = 0;
            double dist = 0;
            bool   break_to_outer_loop = false;

            bool[] is_skipped_at_p = new bool[inputData.Count];
            for (int i = 0; i < inputData.Count; i++)
            {
                is_skipped_at_p[i] = false;
            }

            if (minEntry > maxEntry / 2)
            {
                MessageBox.Show("Requirement: MinNodePerEntry <= MaxNodePerEntry/2");
                return(new List <double> {
                    best_so_far_dist, best_so_far_loc
                });
            }

            List <Rectangle> recList     = new List <Rectangle>();
            List <int>       id_itemList = new List <int>();

            for (int i = 0; i <= inputData.Count - NLength; i++)
            {
                List <double> subseq = inputData.GetRange(i, NLength);
                id_item++;
                Rectangle new_rec = new Rectangle(MathFuncs.PAA_Lower(subseq, D, R).ToArray(), MathFuncs.PAA_Upper(subseq, D, R).ToArray(), i);
                rtree.Add(new_rec, id_item);
                recList.Add(new_rec);
                id_itemList.Add(id_item);
            }


            Dictionary <int, Node <int> > nodeMap   = rtree.getNodeMap();
            List <Node <int> >            leafNodes = nodeMap.Values.Where(node => node.level == 1).OrderBy(node => node.entryCount).ToList();

            List <Rectangle> leafMBRs = leafNodes.Select(node => node.mbr).ToList(); // List rectangle of leaf nodes in order of list leafNodes

            for (int i = 0; i < leafNodes.Count; i++)
            {
                List <Rectangle> leafEntries = leafNodes[i].entries.Where(mbr => mbr != null).Select(mbr => mbr).ToList();
                if (leafEntries.Count > 0)
                {
                    int beginIndex = candidateList.Count;
                    candidateList.AddRange(leafEntries.Select(mbr => mbr.getIndexSubSeq()));
                    beginIndexInner.AddRange(Enumerable.Repeat(beginIndex, leafEntries.Count));
                    indexOfLeafMBRS.AddRange(Enumerable.Repeat(i, leafEntries.Count));
                }
            }

            for (int i = 0; i < candidateList.Count; i++)//outer loop
            {
                int p = candidateList[i];

                // rectangle of subseq in p postion
                if (is_skipped_at_p[p])
                {
                    //p was visited at inner loop before
                    continue;
                }
                else
                {
                    List <double> subseq_p = inputData.GetRange(p, NLength);
                    //Rectangle p_rectangle = recList[p];
                    List <double> P_PAA = MathFuncs.PAA(subseq_p, D);

                    nearest_neighbor_dist = Constants.INFINITE;

                    List <bool> eliminatedMBR = new List <bool>();
                    for (int k = 0; k < leafMBRs.Count; k++)
                    {
                        eliminatedMBR.Add(false);
                    }

                    int indexMBRLeaf   = -1;
                    int num_leaf_skips = 0;

                    for (int j = 0; j < candidateList.Count; j++)// inner loop
                    {
                        // int q = innerList[j];
                        int index_inner = (beginIndexInner[i] + j) % candidateList.Count;
                        int q           = candidateList[index_inner];

                        int index_MBRInnner = (beginIndexInner[i] + j) % candidateList.Count;
                        int MBRInnner       = indexOfLeafMBRS[index_MBRInnner];

                        if (indexMBRLeaf < MBRInnner)//the first entry of the next node ?
                        {
                            indexMBRLeaf++;


                            /* Test:
                             * if (indexMBRInnner[j] == MBRInnner)
                             *  Console.WriteLine("OK");*/

                            //calc minDist:
                            //double minDist = MathFuncss.MINDIST(p_rectangle, leafMBRs[MBRInnner], (NLength / (double)(D)));
                            double minDist = MathFuncs.MINDIST(P_PAA, leafMBRs[MBRInnner], (NLength / (double)(D)));

                            //if (minDist_keo > minDist)
                            //{
                            //   Console.WriteLine("STOPPP");
                            //  return;
                            //}

                            if (minDist >= nearest_neighbor_dist)
                            {
                                num_leaf_skips++;
                                eliminatedMBR[MBRInnner] = true;

                                continue;// pruned => skip to the next one
                            }
                            else
                            {
                                if (Math.Abs(p - q) < NLength)
                                {
                                    continue;// self-match => skip to the next one
                                }

                                //calculate the Distance between p and q
                                dist = MathFuncs.EuDistance(subseq_p, inputData.GetRange(q, NLength));

                                if (dist < best_so_far_dist)
                                {
                                    //skip the element q at oute_loop, 'cuz if (p,q) is not a solution, neither is (q,p).
                                    is_skipped_at_p[q] = true;

                                    break_to_outer_loop = true; //break, to the next loop at outer_loop
                                    break;                      // break at inner_loop first
                                }

                                if (dist < nearest_neighbor_dist)
                                {
                                    nearest_neighbor_dist = dist;
                                }
                            }
                        }
                        else // still the same node
                        {
                            if (eliminatedMBR[MBRInnner]) // can prune ?
                            {
                                continue;
                            }
                            else //do it normally
                            {
                                if (Math.Abs(p - q) < NLength)
                                {
                                    continue;// self-match => skip to the next one
                                }
                                else
                                {
                                    //calculate the Distance between p and q
                                    dist = MathFuncs.EuDistance(subseq_p, inputData.GetRange(q, NLength));

                                    if (dist < best_so_far_dist)
                                    {
                                        //skip the element q at oute_loop, 'cuz if (p,q) is not a solution, neither is (q,p).
                                        is_skipped_at_p[q] = true;

                                        break_to_outer_loop = true; //break, to the next loop at outer_loop
                                        break;                      // break at inner_loop first
                                    }

                                    if (dist < nearest_neighbor_dist)
                                    {
                                        nearest_neighbor_dist = dist;
                                    }
                                }
                            }
                        } //end ELSE
                    }     //end for inner loop

                    //Console.WriteLine("num_leaf_skips="+ num_leaf_skips);
                    if (break_to_outer_loop)
                    {
                        break_to_outer_loop = false; //reset
                        continue;                    //go to the next p in outer loop
                    }

                    if (nearest_neighbor_dist > best_so_far_dist)
                    {
                        best_so_far_dist = nearest_neighbor_dist;
                        best_so_far_loc  = p;
                    }
                }
            }//end outer loop
            if (is_first_time)
            {
                this_id_item     = id_item;
                this_id_itemList = id_itemList;
                this_RTree       = rtree;
                this_rectList    = recList;
            }
            return(new List <double> {
                best_so_far_dist, best_so_far_loc
            });
        }